This invention relates to determination of properties of earth formations surrounding a borehole and, more particularly, to an apparatus and method for determining the velocity of propagation of acoustic wave energy propagating in such formations. Acoustic well logging is widely used to provide information concerning the characteristics of earth formations. Generally, measurements are made of the velocities of acoustic waves to reveal properties, such as porosity, of the formations surrounding a borehole. An acoustic well logging tool for measuring the velocity of acoustic waves typically employs a sonic pulse transmitter and a plurality of sonic receivers selectively spaced from the transmitter. The sonic receivers include transducers to convert the incident acoustic wave to an electrical waveform and suitable amplifiers to transmit the waveforms to surface located processing equipment.
It is well known that the compressional components of the acoustic wave energy generally travel at a higher velocity than the shear components of the acoustic wave energy. It is desirable, at each depth level, to obtain a reading of both the compressional velocity and shear velocity of the acoustic wave energy propagating through the formations since both contribute useful information concerning the formations. When a plurality of spaced receivers are employed, a correlation technique can be used to determine the desired velocity by correlating the signals obtained at the different receivers to obtain an output velocity value which optimally accounts for the difference in arrival times of the signals at the different receiver locations. Briefly, most correlation techniques are based on the assumption that substantially the same signal waveform will arrive at the different receiver locations at different times, the delay as between successively further receiver locations depending upon the distance between receivers and the velocity of propagation of the wave energy in the formations as between the receiver locations. Thus, a correlation technique can be employed to compare a delayed version of a signal arriving at a closer receiver location with a signal arriving at a more remote receiver location, the amount of delay (for a given known distance as between the receivers) depending on an assumed "trial" value of velocity of the acoustic wave energy as between the receiver locations in question. In simplified terms, the correlation technique involves trying various trial velocity values and determining which one provides the best "match".
To visualize a correlation procedure, assume that two signals to be correlated are plotted one-beneath-another on a common time axis, with the lower plotted signal being delayed (advanced in a direction of increasing time on the time axis) with respect to the upper plotted signal. Assume further that the time differential as between the signals (resulting from signal propagation time through formations of unknown nature over a known distance) is unknown. In performing the correlation, the signals are compared using a selected slope to account for the relative time difference between the signals. The selected slope is representative of a trial velocity for the particular correlation since, as previously noted, the time delay as between the two signals (and therefore the slope as between corresponding points on the two signals plotted on the same time axis) is a function of the velocity of propagation of the signals. The comparison is generally done by multiplying the instantaneous values of the two signals at each corresponding point thereof and summing all the products to obtain a single correlation figure. Further correlation figures may then be determined for different trial velocities (or slopes), and the correlation figures may be plotted versus velocity. Ideally, this plot, called a "correlogram" will have a single, well defined peak, the peak (i.e., the single highest correlation figure) indicating the true velocity of propagation of the wave energy. If the wave energy has components which travel at different velocities, multiple peaks may be encountered. Noise and other complications in hostile borehole environment will, of course, also introduce difficulties in interpreting correlograms.
In the copending U.S. patent application Ser. No. 581,381, now abandoned in favor of continuation U.S. application Ser. No. 928,389, now U.S. Pat. No. 4,210,966, of J. Ingram, assigned to the same assignee as the present application, there is disclosed an acoustic logging technique wherein a multiple-fold correlation is utilized; that is, the instantaneous values of three or more signals are multiplied by each other in obtaining each correlation figure. This and other techniques set forth in that application have led to substantial advances in the art, but it is an object of the present invention to provide still further improvements in obtaining accurate values for the velocity of the acoustic wave components of sonic waves propagating in formations surrounding a borehole.